This invention relates generally to a method and apparatus for protecting turbocompressors with sidestreams from the damaging effects of surge. More specifically, the invention relates to a method for estimating the reduced flow rate entering a compression stage that does not have a flow measurement device in its suction or discharge. Reduced flow rate is used to accurately calculate a location of the compression stage""s operating point relative to its surge limit.
To implement accurate and effective antisurge control for turbocompressor stages, a flow measurement is of great value; that is, measuring the flow rate entering or leaving the stage of compression. Turbocompressors with sidestreams, such as ethylene, propylene, and propane refrigeration compressors, pose unique antisurge control challenges. In particular, measurements for the flow rate of fluid entering (or leaving) the compressors"" middle stages are not available in most cases. However, flow rates are often known for the first and/or last compressor stage(s) and the sidestreams.
Present-day control systems for multistage compressors with sidestreams use either of two methods to cope with the lack of flow measurement. In the first method, the control algorithm utilizes an assumption of constant ratios                               (          ZT          )                          2          ⁢          s                                      (          ZT          )                          1          ⁢          d                      =          C      1        ,                              (          ZT          )                          2          ⁢          s                                      (          ZT          )                SS              =          C      2        ,                              (          ZT          )                          2          ⁢          s                                                                                (                ZT                )                                            1                ⁢                d                                      ⁢                          xe2x80x83                        ⁢                                          (                ZT                )                            SS                                      ⁢                  xe2x80x83                      =          C      3      
and calculates an estimate of a differential pressure (for a phantom flow-measurement in the suction of the compressor stage not having a flow measurement) as a function of the differential pressures measured across the existing flow measurement devices. Of course, anytime the above constant ratios are not equal to the originally calculated constant, errors are introduced; furthermore, this method is very cumbersome and difficult to implement.
The second method is described in U.S. Pat. No. 5,599,161 by Batson entitled, xe2x80x9cMethod and Apparatus for Antisurge Control of Multistage Compressors with Sidestreamsxe2x80x9d: instead of reduced flow rate, a different similarity variable is used in which the temperature of the flow into those stages not having flow measurements is unnecessary. When response times of the various measurement devices vary, it is possible that this method could produce false transients.
For the reasons mentioned, there is an obvious need for a simple and accurate antisurge-control algorithm for multistage turbocompressors with sidestreams.
The purpose of this invention is to improve upon the prior art by providing a method whereby the flow rate entering a middle (intermediate) compressor stage can be inferred from known flow rates. One of the keys to accomplishing this flow calculation is the first law of thermodynamics (or the conservation of energy equation):                                                                         ∂                                  xe2x80x83                                                            ∂                t                                      ⁢                                          ∫                                  ∫                  ∫                                            CV                        ⁢            e            ⁢                          xe2x80x83                        ⁢            ρ            ⁢                          xe2x80x83                        ⁢                          ⅆ                              V                _                                              +                                                    ∫                ∫                            CS                        ⁢                          xe2x80x83                        ⁢                          (                              h                +                                                      1                    2                                    ⁢                                      xe2x80x83                                    ⁢                                      V                    2                                                  +                gz                            )                        ⁢                          xe2x80x83                        ⁢            ρ            ⁢                          xe2x80x83                        ⁢                                          V                →                            ·                              ⅆ                                  xe2x80x83                                ⁢                                  A                  →                                                                    =                              Q            .                    +                      W            .                                              (        1        )            
where
t=time
e=specific total energy of the fluid
p=density
=volume
CV=control volume (open system)
CS=control surface (boundary of the control volume)
h=specific enthalpy
V=velocity
g=acceleration of gravity
z=elevation
A=area
{dot over (Q)}=net rate of heat transfer into the control volume
{dot over (W)}=net rate of shaft and shear work into the control volume
Another key to effectuating this invention is a relationship between the pressure and temperature ratios across a compressor. The following is true if the compression process is assumed polytropic:                                           p            s                                ρ            s            n                          =                              p            d                                ρ            d            n                                              (        2        )            
where
p=absolute pressure
s=suction
d=discharge
n=polytropic exponent
Now the equation of state is also invoked:
p=xcfx81ZRTxe2x80x83xe2x80x83(3)
where
Z=compressibility
R=gas constant
T=temperature
Finally, it is easily shown that                                           T            d                                T            s                          =                                            Z              s                                      Z              d                                ⁢                      xe2x80x83                    ⁢                                    (                                                p                  d                                                  p                  s                                            )                                                      n                -                1                            n                                                          (        4        )            
which is the relationship between the temperature and pressure ratios across a compressor when the compression process is assumed polytropic.